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initial value problem y'=ty(4-y)/3, y(0)=y_0 determine the behavior of solution as t increases depends on the...

initial value problem
y'=ty(4-y)/3, y(0)=y_0
determine the behavior of solution as t increases depends on the initial value y_0
The answer says that y->-infinite when y_0<0. but i cannot understand. please explain it

Expert Solution

Using methode of seperable variables,

Using Partial fraction, we can write,

Equating like terms,

When t=0, y(0) = y_0

When,

Let take

THIS VALUE WILL BE ALWAYS POSITIVE.

Lets take y_0= -1

This valus will be always negative .

milcah answered 1 year ago

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